Paper Citation Record · LEDGER

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory

As of 12 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 1 inbound Pith citation observation for arXiv:2601.18258.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2601.18258 v3

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-21T15:31:45.352264Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-21T15:31:45.352264Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-05-21T15:34:15.089476Z

Reference resolution

29 of 29 outbound references displayed

verified exact4
verified fuzzy15
unresolved8
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f682e1f7-681b-48ab-a866-d1d7fb8c5e82 · outbound

This paper cites an unresolved cited work.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-05-21T15:34:15.592002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 468f814d-6c3b-43cf-ab67-50537b838532 · outbound

This paper cites an unresolved cited work.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-05-21T15:34:15.587182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b64160d5-6544-4508-9c92-06fcda9d2086 · outbound

This paper cites Auslander and C.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Auslander and C

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.582252Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 41d97102-9ea6-424f-9a37-8d04996a8820 · outbound

This paper cites an unresolved cited work.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-05-21T15:34:15.589425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 1876eb07-eaff-4a05-bcb2-19defce7d312 · outbound

This paper cites Nilspaces, nilmanifolds and their morphisms.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Nilspaces, nilmanifolds and their morphisms

Reference 5

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T15:34:15.110096Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f8727455-e11b-49bf-9d8e-7cadeffa14a8 · outbound

This paper cites Connes and D.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Connes and D

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.584485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 94d0d611-e7f7-4c18-9e23-63670607cfc3 · outbound

This paper cites Etingof, S.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Etingof, S

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.579977Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6cdd80c2-a10d-4de8-a67c-63109c66e4e4 · outbound

This paper cites Faith,Algebra: Rings, modules and categories.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Faith,Algebra: Rings, modules and categories

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.577509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d598bf71-b8f1-4695-8291-2d48948db7f8 · outbound

This paper cites an unresolved cited work.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-05-21T15:34:15.594531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4c11efab-d23d-4726-8935-7a26049b4e8b · outbound

This paper cites Gildea,Algebraic phase theory i: Radical phase geometry and structural boundaries, 2026, Available at.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Gildea,Algebraic phase theory i: Radical phase geometry and structural boundaries, 2026, Available at

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-21T15:34:15.102257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 74300737-3f53-4ce5-9d24-af59e93db93d · outbound

This paper cites Gildea,Algebraic phase theory ii: The frobenius–heisenberg phase and boundary rigidity, 2026, Available at.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Gildea,Algebraic phase theory ii: The frobenius–heisenberg phase and boundary rigidity, 2026, Available at

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-21T15:34:15.094609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 01e96371-3972-4e72-bc4c-82db494e4ae5 · outbound

This paper cites Gildea,Algebraic phase theory iii: Structural quantum codes over frobenius rings, 2026, Available at.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Gildea,Algebraic phase theory iii: Structural quantum codes over frobenius rings, 2026, Available at

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-21T15:34:15.106526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4bdf68ac-95cd-48e1-8188-e7063b75505e · outbound

This paper cites Gildea,Algebraic phase theory iv: Morphisms, equivalences, and categorical rigidity, 2026, Available at.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Gildea,Algebraic phase theory iv: Morphisms, equivalences, and categorical rigidity, 2026, Available at

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-21T15:34:15.098550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 02755cc9-eb29-47fd-9ac9-f2ae1c170d97 · outbound

This paper cites Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory

Reference 14

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T15:34:15.090863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8f45e376-ed9a-411f-a7f0-5befdd3ebc5b · outbound

This paper cites an unresolved cited work.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-05-21T15:34:15.564939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e6c60c26-5a62-4ed2-8db6-b64561a2aa67 · outbound

This paper cites Green and T.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Green and T

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.562369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ab26606c-1d31-4c62-bfc7-2da779fc8fef · outbound

This paper cites Green, T.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Green, T

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.555166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 51806301-e01a-4b85-aa32-3fb2a1332e88 · outbound

This paper cites 12, 122107.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory 12, 122107

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.557350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8d87e944-da2a-45b6-a375-ee6a4f6c4d58 · outbound

This paper cites Extraits du S´ eminaire Bour- baki 1957-1962, Paris: Secr´ etariat math´ ematique (1962).

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Extraits du S´ eminaire Bour- baki 1957-1962, Paris: Secr´ etariat math´ ematique (1962)

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.559921Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8ac9ecef-24dc-48ca-97ec-2c5ab292330d · outbound

This paper cites Honold,Characterization of finite Frobenius rings, Arch.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Honold,Characterization of finite Frobenius rings, Arch

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.567763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6a534220-e790-45ba-b06e-312a3672706b · outbound

This paper cites Howe,On the role of the Heisenberg group in harmonic analysis, Bull.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Howe,On the role of the Heisenberg group in harmonic analysis, Bull

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.570687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 59365eb6-829f-432d-8984-52c5dd7279ef · outbound

This paper cites Martin Isaacs,Character theory of finite groups., corrected reprint of the 1976 original ed., Providence, RI: AMS Chelsea Publishing, 2006 (English).

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Martin Isaacs,Character theory of finite groups., corrected reprint of the 1976 original ed., Providence, RI: AMS Chelsea Publishing, 2006 (English)

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.574379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 7bc9b39b-e8bd-46c3-bc72-48c3ec9b63c8 · outbound

This paper cites Jacobson,Structure of rings, American Mathematical Society Colloquium Publications, vol.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Jacobson,Structure of rings, American Mathematical Society Colloquium Publications, vol

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.538102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8a43a5a2-83b6-4f4c-b142-af17433271b7 · outbound

This paper cites an unresolved cited work.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-05-21T15:34:15.550164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f47a384e-b759-42d5-84e4-aee0c066627d · outbound

This paper cites an unresolved cited work.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-05-21T15:34:15.552901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c2b44a45-8bc8-4d7a-adfd-bae2d079d798 · outbound

This paper cites Translated from the French by Leonard L.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Translated from the French by Leonard L

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.545404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a9092925-9bbf-4129-b8c8-ea0cf02b8518 · outbound

This paper cites Tao and V.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Tao and V

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.542879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 04ccffa0-c9c3-49f4-9528-b5c95da3d833 · outbound

This paper cites Weil,Sur certains groupes d’op´ erateurs unitaires, Acta Math.111(1964), 143–211 (French).

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Weil,Sur certains groupes d’op´ erateurs unitaires, Acta Math.111(1964), 143–211 (French)

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T15:34:15.547727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6814c298-d4e4-4805-a397-c3a16ac604e2 · outbound

This paper cites an unresolved cited work.

Duality, Reconstruction, and Structural Toolkit Theorems in Algebraic Phase Theory Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-05-21T15:34:15.540493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

Observation 02755cc9-eb29-47fd-9ac9-f2ae1c170d97 · inbound